Q 25 Use the Maclaurin series for cos... [FREE SOLUTION]

Chapter 8: Q 25 (page 704)

Use the Maclaurin series for $\cos x, \sin x$ and $e^{x}$ to find the values of the following series.
$蟺 - \frac{蟺^{3}}{3!} + \frac{蟺^{5}}{5!} - \frac{蟺^{7}}{7!} + 鈰�$

Short Answer

Expert verified

The values of the series $蟺 - \frac{蟺^{3}}{3!} + \frac{蟺^{5}}{5!} - \frac{蟺^{7}}{7!} + 鈰�$ is $蟺 - \frac{蟺^{3}}{3!} + \frac{蟺^{5}}{5!} - \frac{蟺^{7}}{7!} + 鈰� = 0$

Step by step solution

Given information

The series is $蟺 - \frac{蟺^{3}}{3!} + \frac{蟺^{5}}{5!} - \frac{蟺^{7}}{7!} + 鈰�$

Find the Maclaurin series for the function f(x)=sinx

The Maclaurin series for the function $f (x) = \sin x$ is

$\sin x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} + 鈰�$

The series $蟺 - \frac{蟺^{3}}{3!} + \frac{蟺^{5}}{5!} - \frac{蟺^{7}}{7!} + 鈰�$ is the Maclaurin series for $\sin x$ at $x = 蟺$

Find the values of the series.

$x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} + 鈰� = \sin x$

Therefore,

$蟺 - \frac{蟺^{3}}{3!} + \frac{蟺^{5}}{5!} - \frac{蟺^{7}}{7!} + 鈰� = \sin 蟺蟺 - \frac{蟺^{3}}{3!} + \frac{蟺^{5}}{5!} - \frac{蟺^{7}}{7!} + 鈰� = 0$

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91影视

Use the Maclaurin series for $\cos x, \sin x$ and $e^{x}$ to find the values of the following series.
$蟺 - \frac{蟺^{3}}{3!} + \frac{蟺^{5}}{5!} - \frac{蟺^{7}}{7!} + 鈰�$

Short Answer

Step by step solution

Given information

Find the Maclaurin series for the function f(x)=sinx

Find the values of the series.

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91影视

Use the Maclaurin series for cosx,sinxand ex to find the values of the following series.蟺-蟺33!+蟺55!-蟺77!+鈰�

Short Answer

Step by step solution

Given information

Find the Maclaurin series for the function f(x)=sinx

Find the values of the series.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Decision Maths

Logic and Functions

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use the Maclaurin series for $\cos x, \sin x$ and $e^{x}$ to find the values of the following series.
$蟺 - \frac{蟺^{3}}{3!} + \frac{蟺^{5}}{5!} - \frac{蟺^{7}}{7!} + 鈰�$